Two-loop QCD corrections of the massive fermion propagator

TL;DR

This paper provides a complete two-loop calculation of the off-shell massive quark propagator in QCD within a general covariant gauge, using generalized recurrence relations to reduce two-loop integrals to a compact set of master integrals. It delivers both bare and MSbar-renormalized amplitudes, enabling a precise extraction of the pole mass to MSbar mass relation by locating the pole of the MSbar-renormalized propagator, and it confirms agreement with established results for the two-loop mass relation. The renormalized results exhibit cancellations of many transcendental structures, highlighting a robust final expression suitable for scheme matching and decoupling analyses. The methods and results provide a cross-check for on-shell recurrence approaches and connect with MOM-scheme NNLO calculations, with implications for heavy-quark physics and lattice QCD renormalization across schemes and dimensions.

Abstract

The off-shell two-loop correction to the massive quark propagator in an arbitrary covariant gauge is calculated and results for the bare and renormalized propagator are presented. The calculations were performed by means of a set of new generalized recurrence relations proposed recently by one of the authors. From the position of the pole of the renormalized propagator we obtain the relationship between the pole mass and the \bar{MS} mass. This relation confirms the known result by Gray et al.. The bare amplitudes are given for an arbitrary gauge group and for arbitrary space-time dimensions.